The field of the invention is motor controllers for controlling the speed of high performance electrical induction motors and, more particularly, the invention relates to a method and apparatus for determining a motor's transient inductance which is used during motor control.
Induction Motors
Induction motors generally include a rotor mounted inside a stator for rotation about a rotation axis. A common rotor design includes a "squirrel cage winding" in which axial conductive bars are connected at either end by shorting rings to form a generally cylindrical structure. The stator is formed by a plurality of windings which surround the rotor and are typically arranged in three separate phases. Time varying voltage is applied across the stator windings which generate an electromotive force (emf) and an associated stator magnetic field which rotates around the stator at a stator field frequency primarily within the space defined by the rotor. As the stator field rotates about the rotor, relative motion between the stator field flux and the rotor bars induces voltages in the rotor.
The voltages induced in the rotor cause rotor bar currents which in turn generate a rotor magnetic field. The stator and rotor fields are stationary with respect to each other but are separated by a changeable rotor angle .alpha.. The two fields interact to produce torque which causes rotor rotation.
Ideally, rotor speed should be controllable by simply controlling the stator field frequency. For example, because the rotor follows the stator field, by increasing stator field frequency the rotor frequency should also increase. Unfortunately, while the general rule that rotor frequency can be controlled by controlling stator field frequency is accurate, the motor is non-linear which makes precise control extremely complex.
Field-Oriented Control of Induction Machines
Referring to FIG. 1, a rotating phasor 14 corresponding to the stator magneto motive force ("mmf") forms an angle .alpha. with respect to a phasor corresponding to rotor flux 18. Torque generated by the motor is proportional to the magnitudes of these phasors 14 and 18 but also is a function of angle .alpha.. Maximum torque is produced when phasors 14 and 18 are at right angles to each other (e.g., .alpha.=90.degree. ) whereas zero torque is produced if these phasors are aligned (e.g., .alpha.=0.degree. ). Phasor 14 may therefore be usefully decomposed into a torque producing component 15 perpendicular to phasor 18 and a flux component 17 parallel to phasor 18.
Mmf components 15 and 17 are proportional, respectively, to two stator currents i.sub.qe, a torque producing current, and i.sub.de, a flux producing current, which may be represented by orthogonal vectors in the rotating frame of reference (synchronous frame of reference) of the stator flux having slowly varying magnitudes. The subscript "e" is used to indicate that a particular quantity is in the rotating or synchronous frame of stator flux.
Accordingly, in induction motor control, in addition to controlling the stator voltage frequency (i.e. the rotational speed of phasor 13) and stator voltage amplitude, it is also advantageous to control the stator voltage phase relative to the stator winding current and hence division of stator winding current into i.sub.qe and i.sub.de components. Control strategies that attempt to independently control currents i.sub.qe and i.sub.de are generally termed field oriented control strategies ("FOC") and require knowledge about both i.sub.de and i.sub.qe magnitudes and an associated slip frequency.
One common way to control division of the d and q-axis currents i.sub.de and i.sub.qe is to employ a model reference adaptive controller (MRAC). An MRAC receives motor command signals and derives motor reference quantities based on the command signals. The reference quantities are compared to the actual motor feedback quantities to generate error signals. The error signals are used by an adaptive controller mechanism to alter controller gains and thereby eliminate the error and, in the case of FOC, maintain field orientation.
An MRAC requires an accurate model of the plant to be controlled. Therefore, to be accurate, the MRAC must be provided with certain characteristic motor parameters which can be used to define outputs corresponding to specific motor input command signals.
Generally, the production of any given set of currents i.sub.qe and i.sub.de requires that the stator be excited with voltages V.sub.qe and V.sub.de as follows: EQU V.sub.qe =r.sub.s i.sub.qe +.omega..sub.e .lambda..sub.de Eq. 1 EQU V.sub.de =r.sub.s i.sub.de -.omega..sub.e .lambda..sub.qe Eq. 2
where, EQU V.sub.qe, V.sub.de =terminal voltage components; EQU r.sub.s =stator resistance; EQU i.sub.qe, i.sub.de =terminal current components; EQU .omega..sub.e =electrical field frequency; and EQU .lambda..sub.de, .lambda..sub.qe =stator flux linkages
and where, EQU r.sub.s i.sub.de, r.sub.s i.sub.qe =stator resistance voltage drops;
and
.omega..sub.e .lambda..sub.de, .omega..sub.e .lambda..sub.qe =counter electromotive forces (EMFs). In addition, motor torque can be represented by the equation: ##EQU1##
As well known in the FOC art: EQU .lambda..sub.de =L.sub.s i.sub.de Eq. 4
and EQU .lambda..sub.qe =L.sub..sigma. i.sub.qe Eq. 5
where EQU L.sub.s motor winding inductance and EQU L.sub..sigma. =transient inductance
Combining Equations 2 and 5: EQU V.sub.de =r.sub.s i.sub.de -.omega..sub.e L.sub..sigma. i.sub.qe Eq. 6
Clearly, based on Equation 6, one important characteristic motor parameter for model reference adaptive FOC is transient inductance L.sub..sigma.. The industry has derived numerous tests which can be used to provide an inductance estimate L.sub..sigma. and has provided various control schemes which can be used to adjust motor control as a function of the estimate. One particularly useful test which provides an L.sub..sigma. estimate during a commissioning procedure prior to normal motor operation is described in U.S. patent application Ser. No. 08/402,288 which was filed on Mar. 10, 1995 which is entitled TRANSIENT INDUCTANCE IDENTIFIER FOR MOTOR CONTROL and which is incorporated herein by reference. Once the procedure described therein yields an inductance estimate, the estimate is used for motor control during normal operation.
Drive performance, including torque and flux control and field orientation generally depend upon the accuracy of the L.sub..sigma. estimate. For example, if estimate L.sub..sigma. is in error, flux .lambda..sub.qe is in error (see Equation 5) and voltage V.sub.de is in error (see Equation 2) and the motor torque Te is also in error (see Equation 3). For example, if estimate L.sub..sigma. is too large, according to Equation 5, flux .lambda..sub.qe will be too large. Flux .lambda..sub.qe is increased at the expense of flux .lambda..sub.de. Thus, if flux .lambda..sub.qe is too large because estimate L.sub..sigma. is too large, then flux .lambda..sub.de will be too small and the q-axis stator voltage V.sub.qe will be too small (see Equation 1). For this reason, voltage V.sub.qe can be used as an indicator of transient inductance error. Here, where V.sub.qe is too small, the inductance estimate is too large and vice versa. These relationships can be illustrated by comparing motor operating quantities derived with a correct L.sub..sigma. value (FIG. 2) and an incorrect value (FIG. 3).
FIG. 2 shows the transient response of a current regulated induction motor drive operating under torque control with a correct L.sub..sigma. value. The motor is field oriented, torque Te is commanded without oscillation and very little error develops in the q-axis stator voltage V.sub.qe or rotor flux .lambda..sub.qr.
FIG. 3, however, shows results derived using the same control system, but with an L.sub..sigma. estimate which is 85% of the motor's actual transient inductance. Errors appear in each of the torque Te, q-axis stator voltage V.sub.qe and q-axis rotor flux .lambda..sub.qr. In addition, it takes a relatively long time for transients to decay.
As well known in the art, torque producing current i.sub.qe changes with load. Furthermore, inductance L.sub..sigma. is load dependant (see FIG. 5). For this reason, while the commissioning test described in the above referenced patent application provides a fairly accurate initial L.sub..sigma. estimate, during motor operation actual L.sub..sigma. can change appreciably thereby distorting field orientation. In some cases actual L.sub..sigma. can be greater than +/- 15% different than the estimate.
Referring to FIG. 4, the effect of an L.sub..sigma. error on q and d-axis reference voltages during a load step is illustrated. The AC motor used in this test was a 75 Hp, 460 V, 1783 rpm, 85 Arms machine. At 10 seconds a 1 p.u. torque step was applied with a DC dyne running as a velocity regulator at 1500 rpm. At the 10 second point initial oscillation in the voltages is due to L di/dt which is not compensated for in the model reference adaptive control.
Following the inductance transient, a low frequency oscillation at slip frequency occurs since field orientation is not achieved. Once steady state is reached, it is evident from the drop in q-axis voltage that field orientation is lost. If field orientation had been achieved the q-axis voltage should increase by i.sub.qe *r.sub.s (see Equation 1).
Thus, it should be appreciated that even a small error in the L.sub..sigma. estimate causes controller error and the loss of FOC. Therefore, it would be advantageous to have a system which facilitates precise field oriented control despite changes in the actual transient inductance L.sub..sigma..